Examine the following statements:

1. All colours are pleasant.

2. Some colours are pleasant.

3. No colour is pleasant.

4. Some colours are not pleasant.

Given that statement 4 is true, what can be definitely concluded?

Correct Answer: The correct option is 1 is false.

Step-by-step Explanation:

Let us analyze the given logical statements and their relationships based on categorical logic:

1. Statement 1: "All colours are pleasant." (Universal Affirmative - A proposition)
2. Statement 2: "Some colours are pleasant." (Particular Affirmative - I proposition)
3. Statement 3: "No colour is pleasant." (Universal Negative - E proposition)
4. Statement 4: "Some colours are not pleasant." (Particular Negative - O proposition)

We are given that Statement 4 ("Some colours are not pleasant") is TRUE.

According to the traditional Square of Opposition in logic:

- Contradictory Relationship: Statement 1 ("All colours are pleasant") and Statement 4 ("Some colours are not pleasant") are contradictories of each other. Two contradictory statements cannot both be true, nor can they both be false. If one is true, the other must be false.

Since Statement 4 is given as TRUE, its contradictory, Statement 1 ("All colours are pleasant"), must definitely be FALSE.

Therefore, we can definitely conclude that 1 is false.